基于改进粒子群优化的非线性最小二乘估计

Nonlinear least squares estimation based on improved particle swarm optimization

针对测量数据处理中非线性模型参数估计理论广泛使用的传统牛顿类算法对初值的敏感性问题,提出了一种求解非线性最小二乘估计的改进粒子群优化算法。该算法利用均匀设计方法在可行域内产生初始群体,无需未知参数θ的较好的近似作为迭代初值,而具有大范围收敛的性质;通过偏转、拉伸目标函数有效地抑制了粒子群优化算法易收敛到局部最优的缺陷。给出应用该方法到NLSE的具体步骤,通过仿真实验证明该算法的有效性。

To investigate the sensitivity of the traditional Newton methods widely used in the theory of nonlinear least squares estimation （NLSE） in geodesic data processing to the initial point, an improved particle swarm optimization （PSO） algorithm is proposed. It generates the initial population in feasible field by uniform design method, so it has the property of convergence in large scale without better approximation of the unknown parameter θ as iterative initial point. It restrains PSO＇ s local convergence limitation efficiently by deflection and stretching of objective function. Finally the detailled steps of the proposed method for NLSE are given, and experiments done show the improved technique＇s effectiveness.